The Kalman Filter is a specialized implementation of the Bayesian Filter. It is widely used in various engineering fields due to its optimality and computational efficiency when applied to linear systems with Gaussian noise. Below is a step-by-step mathematical derivation of its update equatio...
Image denoising is a fundamental task in computer vision, aiming to recover a clean image from a noisy observation. Total variation minimization, introduced by Rudin, Osher, and Fatemi (ROF), addresses this by penalizing the image gradient and data fidelity. This post explores the mathematical...
This article explains how to solve roots of a quartic polynomial in the complex plane. I use the depressed form of the quartic polynomial and Descartes’ method. Additionally, I demonstrate an interactive demo which visualizes the roots of a quartic polynomial.
This article explains how to solve roots of a cubic polynomial in the complex plane. I use the depressed form of the cubic polynomial and Cardano’s formula. Additionally, I demonstrate an interactive demo which visualizes the roots of a cubic polynomial.
This post delves into the specifics of various camera models, exploring the mathematical and geometric concepts used to represent how a camera captures the world. However, when capturing world scenes through a camera, images suffer from distortions due to the physical properties of the lens. T...